Question: Simplify the following expression: $\dfrac{7q^3}{9q}$ You can assume $q \neq 0$.
Explanation: $ \dfrac{7q^3}{9q} = \dfrac{7}{9} \cdot \dfrac{q^3}{q} $ To simplify $\frac{7}{9}$ , find the greatest common factor (GCD) of $7$ and $9$ $7 = 7$ $9 = 3 \cdot 3$ $ \mbox{GCD}(7, 9) = = 1 $ $ \dfrac{7}{9} \cdot \dfrac{q^3}{q} = \dfrac{1 \cdot 7}{1 \cdot 9} \cdot \dfrac{q^3}{q} $ $\phantom{ \dfrac{7}{9} \cdot \dfrac{3}{1}} = \dfrac{7}{9} \cdot \dfrac{q^3}{q} $ $ \dfrac{q^3}{q} = \dfrac{q \cdot q \cdot q}{q} = q^2 $ $ \dfrac{7}{9} \cdot q^2 = \dfrac{7q^2}{9} $